prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{3 x}
g(x) = 2 \cos{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \cos{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 2 x + 1
g(x) = 3 x^{2} + 3 x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{3 x}
g(x) = x^{2} + x + 3
Compute: f▽g = f(x) + g''(x)
at x = -1.94
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + x + 1
g(x) = 3 \cos{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \cos{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + 2 x + 1
g(x) = x^{2} + 3 x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = \cos{\left(3 x \right)}
g(x) = 2 x^{2} + 3 x + 1
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

f_latex: \cos{\left(3 x \right)}

expected_str: \cos{\left(3 x \right)} + 4


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{2 x}
g(x) = \sin{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: \sin{\left(x \right)}

expected_str: e^{2 x} - \sin{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{x}
g(x) = x^{2} + 2 x + 3
Compute: f▽g = f(x) + g''(x)
at x = -1.66
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + 3 x + 1
g(x) = 2 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \cos{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + 3 x + 2
g(x) = 3 \log{\left(x e^{2} \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(x e^{2} \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \sin{\left(x \right)}
g(x) = \log{\left(e x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

f_latex: 3 \sin{\left(x \right)}

g_latex: \log{\left(e x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \cos{\left(2 x \right)}
g(x) = 2 x^{2} + 2 x + 1
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

f_latex: 2 \cos{\left(2 x \right)}

expected_str: 2 \cos{\left(2 x \right)} + 4


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 2 x + 1
g(x) = \log{\left(10 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: \log{\left(10 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + 2 x + 2
g(x) = 3 \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(100 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{2 x}
g(x) = 3 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \cos{\left(x \right)}

expected_str: 3 e^{2 x} - 3 \cos{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + x + 3
g(x) = 2 \sin{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \sin{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + x + 2
g(x) = 2 x^{2} + x + 1
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + x + 2
g(x) = 2 x^{2} + 2 x + 1
Compute: f▽g = f(x) + g''(x)
at x = -2.31
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \sin{\left(2 x \right)}
g(x) = 3 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

f_latex: 2 \sin{\left(2 x \right)}

expected_str: \left(4 \sin{\left(x \right)} - 3\right) \cos{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{x}
g(x) = 3 \log{\left(x e^{3} \right)}
Compute: f▽g = f(x) + g''(x)
at x = -2.59
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(x e^{3} \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \cos{\left(2 x \right)}
g(x) = 2 \log{\left(10 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \log{\left(10 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{x}
g(x) = 2 x^{2} + x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + 2 x + 1
g(x) = 3 \log{\left(e x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(e x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{3 x}
g(x) = 3 x^{2} + 2 x + 1
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{2 x}
g(x) = 3 x^{2} + 2 x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{2 x}
g(x) = \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: \log{\left(100 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \sin{\left(x \right)}
g(x) = x^{2} + 2 x + 1
Compute: f▽g = f(x) + g''(x)
at x = -0.1
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \sin{\left(3 x \right)}
g(x) = 2 \log{\left(x e^{3} \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

f_latex: 2 \sin{\left(3 x \right)}

g_latex: 2 \log{\left(x e^{3} \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + 3 x + 3
g(x) = 2 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 0.97
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{3 x}
g(x) = 3 x^{2} + x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + 3 x + 1
g(x) = 2 \log{\left(e x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \log{\left(e x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{3 x}
g(x) = \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 2.09
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{3 x}
g(x) = 3 x^{2} + x + 3
Compute: f▽g = f(x) + g''(x)
at x = -0.79
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{3 x}
g(x) = \sin{\left(2 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: \sin{\left(2 x \right)}

expected_str: 2 e^{3 x} - 4 \sin{\left(2 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{x}
g(x) = 3 \log{\left(x e^{3} \right)}
Compute: f▽g = f(x) + g''(x)
at x = -1.13
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{3 x}
g(x) = 3 \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = \sin{\left(2 x \right)}
g(x) = 2 x^{2} + 3 x + 2
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

f_latex: \sin{\left(2 x \right)}

expected_str: \sin{\left(2 x \right)} + 4


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \cos{\left(2 x \right)}
g(x) = 3 x^{2} + 2 x + 3
Compute: f▽g = f(x) + g''(x)
at x = 1.43
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + 3 x + 3
g(x) = 3 \log{\left(10 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -0.17
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(10 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{x}
g(x) = 2 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

expected_str: 2 e^{x} - 2 \cos{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{2 x}
g(x) = 2 \log{\left(10 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 0.52
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{2 x}
g(x) = \log{\left(x e^{2} \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: \log{\left(x e^{2} \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{2 x}
g(x) = 2 x^{2} + 3 x + 1
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + 3 x + 1
g(x) = \sin{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: \sin{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \cos{\left(3 x \right)}
g(x) = 2 x^{2} + 2 x + 1
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

f_latex: 2 \cos{\left(3 x \right)}

expected_str: 2 \cos{\left(3 x \right)} + 4


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 2 x + 2
g(x) = \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{x}
g(x) = x^{2} + 2 x + 2
Compute: f▽g = f(x) + g''(x)
at x = -0.6
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 2 x + 2
g(x) = x^{2} + x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \cos{\left(3 x \right)}
g(x) = 3 \sin{\left(2 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 0.95
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: 3 \cos{\left(3 x \right)}

g_latex: 3 \sin{\left(2 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 2 x + 2
g(x) = 3 \sin{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \sin{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 2 x + 1
g(x) = 2 x^{2} + 2 x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{x}
g(x) = x^{2} + 3 x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{2 x}
g(x) = 2 \log{\left(e x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{x}
g(x) = \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{3 x}
g(x) = 3 x^{2} + 3 x + 2
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{2 x}
g(x) = 2 x^{2} + 3 x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \cos{\left(3 x \right)}
g(x) = 3 \cos{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \cos{\left(3 x \right)}

expected_str: - 25 \cos{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + x + 1
g(x) = x^{2} + 2 x + 3
Compute: f▽g = f(x) + g''(x)
at x = 2.46
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \cos{\left(3 x \right)}
g(x) = 2 x^{2} + 3 x + 2
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

expected_str: 3 \cos{\left(3 x \right)} + 4


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + 2 x + 2
g(x) = 2 x^{2} + x + 2
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{x}
g(x) = x^{2} + x + 2
Compute: f▽g = f(x) + g''(x)
at x = 1.83
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + x + 3
g(x) = \sin{\left(2 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -2.41
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + 3 x + 2
g(x) = 2 \cos{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -0.49
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \cos{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + 3 x + 3
g(x) = 3 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -2.84
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]